Question: Solve for $x$, $ \dfrac{x + 8}{15x + 5} = -\dfrac{4}{3x + 1} - \dfrac{4}{15x + 5} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $15x + 5$ $3x + 1$ and $15x + 5$ The common denominator is $15x + 5$ The denominator of the first term is already $15x + 5$ , so we don't need to change it. To get $15x + 5$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ -\dfrac{4}{3x + 1} \times \dfrac{5}{5} = -\dfrac{20}{15x + 5} $ The denominator of the third term is already $15x + 5$ , so we don't need to change it. This give us: $ \dfrac{x + 8}{15x + 5} = -\dfrac{20}{15x + 5} - \dfrac{4}{15x + 5} $ If we multiply both sides of the equation by $15x + 5$ , we get: $ x + 8 = -20 - 4$ $ x + 8 = -24$ $ x = -32 $